Multivariate Polynomial Interpolations Arising by Hyperplanes

1993 ◽  
pp. 206-230
Author(s):  
B. D. Bojanov ◽  
H. A. Hakopian ◽  
A. A. Sahakian
Keyword(s):  
Multivariate Polynomial

scholarly journals Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?

2020 ◽  
Vol 14 (1) ◽  
pp. 293-306
Author(s):  
Claire Delaplace ◽  
Alexander May
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Discrete Logarithm ◽  
Field Size ◽  
Square Root ◽  
Multivariate Polynomial ◽  
Bivariate Polynomial ◽  
Testing Problem ◽  
Polynomial Zero ◽  
Representation Technique

AbstractWe give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields a p1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to an o(p)-algorithm for ECDLP, since all involved lists are of size as small as $\begin{array}{} p^{\frac 3 4}, \end{array}$ only their computation is yet too costly.

scholarly journals Accelerated Solution of Multivariate Polynomial Systems of Equations

2003 ◽  
Vol 32 (2) ◽  
pp. 435-454 ◽  
Author(s):  
B. Mourrain ◽  
V. Y. Pan ◽  
O. Ruatta
Keyword(s):  
Polynomial Systems ◽  
Systems Of Equations ◽  
Multivariate Polynomial
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